The critical compressive load in the buckling of circular and annular composite plates reinforced with carbon nanotubes(CNTs) is calculated using finite element method. The developed model is based on the third-order shear deformation theory for moderately thick laminated plates. Effects of CNTs orientation angles and thickness-to-inner radius ratio on the buckling of composite plate are discussed. The results arc compared with those obtained by analytical method based on classical plate theory. The finite clement method shows lower values for critical buckling load because of the elimination of shear strain in the classical plate theory.